When I was in college, I recall, reading about a British program called HOTOL (Horizontal Take-Off and Landing, click picture to be taken to a page on it) which was supposed to use a “liquid air” engine in order to more efficiently reach orbit.
A short description of the cycle was that it was fueled with LH2 and for much of the way up, it would use the cold liquid hydrogen to extract liquid oxygen out of the air.
It got canceled, or more accurately, when the program ended it was not taken to the next phase.
I kind of figured that technical issues, my guess at the time (which appears to be wrong) was getting the heat exchangers small enough and light enough.
The real problem appeared to be that the engine was heavy, and in an aft mounting configuration, maintaining the center of lift far enough aft compromised performance.
In any case, a company called Reaction Engines are having another go at the concept with the Skylon, (paid subscription required) , which uses the Sabre (Synergic Air-Breathing Engine).*
As is clear from the picture, they dealt with the CG issues by placing the heavy engines at the center of lift on the wing tips.
It’s supposed to function as an air-breather until it reaches 30km altitude and “around Mach 5”, and then function as a normal liquid fueled rocket the rest of the way up to orbit.
They are looking at testing a 9% scale precooler (left) in January on a test stand, using a RR Viper turbojet behind the cooler (left below)
There are two problems with Liquid Air Cycle Engines (LACE), hydrogen embrittlement of the heat exchanger, and condensation of water and CO2 on the heat exchanger, which will plug it up.
It solves these problems by not cooling the air to full liquid state, but instead having a high-pressure turbo compressor behind the air to liquefy it, and by using helium as an intermediate medium for the heat exchanger, along with an unspecified proprietary frost control technique. (bottom pic)
It’s a neat concept, but I’m dubious of any project that is not fully funded, or almost fully funded by government sources, and at this point, they are getting just a trickle from the British National Space Center and the the European Space Agency (ESA).
*Let me note here that the Brits come up with cool names.